Question

SECTION 4.3 Polynomial Division; The Factor the polynomial function f(x). Then solve the equation f(x) = 0. 39, f(x) =x3 + 4x2 + x-6 40. fx) 5x - 2x 24 41, f(x) =x3-6x2 + 3x+10 42. f(x)-x3 + 2x2-13x + 10 43, f(x) = x3-x2-14x + 24 44.f(x) = x3-3x2 In Ex given. a): Fi b) C in gi - L 二 10x +24ー丁only, this one d) C gi ase 45' f(x) =x4-7x3 + 9x2 + 27x-54 plecs( 46, f(x) = x4-4x3-7x2 + 34x-24 47, f(x) x4-x3-19x2 + 49x-30 48, f(x) x4 + 11x3 + 41x2 + 61x + 30 Sketch the procedure outlined on p. 240. Use synthetic division and the 62. graph of the polynomial function. Follow the remainder theorem to find the zeros. 49. f(x) = x4-x3-7x2 + x + 6 63. 51, f(x) = x3-7x + 6 52, f(x) = x3-12x + 16

Answer 1

f(x) = x^3 - 3x^3 - 10x + 24 f(2) = 8 - 12 - 20 + 24 = 0 doublerightarrow x = 2 (one solution) using synthetic division. Doublerightarrow f(x) = (x - 2) (x^2 - x - 12) f(x) = (x - 2) (x^2 - 4x + 3x - 12) f(x) = (x - 2) (x(x - 4) + 3 (x - 4)) f(x) = (x - 2) (x - 4) (x + 3) factor form. Now solve f(x) = 0 doublerightarrow (x - 2) (x - 4) (x + 3) = 0 doublerightarrow x = - 3, x = 2, x = 4